{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 4.1 (Page 154)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.arange(-2, 2, 0.01)\n",
    "degree = np.arange(5)\n",
    "for i in degree:\n",
    "    y = x ** i\n",
    "    label = 'x**'+str(i)\n",
    "    plt.plot(x, y, label=label)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 4.3 (Page 154)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def L(k, x):\n",
    "    if k == 0:\n",
    "        return [1]\n",
    "    elif k == 1:\n",
    "        return [1, x]\n",
    "    else:\n",
    "        temp = L(k-1, x)\n",
    "        lkx = (2 * k - 1) / k * x * temp[-1] - (k - 1) / k * temp[-2]\n",
    "        temp.append(lkx)\n",
    "        return temp\n",
    "\n",
    "X = np.arange(-1, 1, 0.05)\n",
    "Y = []\n",
    "for x in X:\n",
    "    y = L(6, x)\n",
    "    Y.append(y)\n",
    "Y = np.array(Y)\n",
    "\n",
    "for k in range(7):\n",
    "    plt.plot(X, Y[:, k], label=\"L\"+str(k)+\"(x)\")\n",
    "    plt.legend()\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"degree\")\n",
    "plt.title(\"Legendre Polynomial\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 4.4 (Page 155)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E2=2.082396716905117\n",
      "E10=2.1130425056211815\n",
      "E10-E2=0.03064578871606427\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "from scipy.integrate import quad\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus']=False #用来正常显示负号\n",
    "\n",
    "#参数\n",
    "Qf = 5\n",
    "N = 100\n",
    "sigma2 = 1\n",
    "\n",
    "#### Step 1:数据准备\n",
    "\n",
    "#定义勒让德多项式，产生L(0,x),...,L(k,x),注意这里不要用递归\n",
    "def L(k,x):\n",
    "    if(k == 0):\n",
    "        return [1.0]\n",
    "    elif(k == 1):\n",
    "        return [1.0, x * 1.0]\n",
    "    else:\n",
    "        result = [1, x]\n",
    "        for i in range(2,k+1):\n",
    "            s = (2 * i - 1) / i * (x * result[-1]) - (i - 1) / i * result[-2]\n",
    "            result.append(s)\n",
    "        return result\n",
    "\n",
    "#系数ai\n",
    "a = np.random.normal(size=Qf+1)\n",
    "\n",
    "#标准化\n",
    "k = np.arange(1, 2*Qf+2, 2)\n",
    "s = (2 * a**2 / k).sum()\n",
    "a = a / np.sqrt(s)\n",
    "\n",
    "#产生点集\n",
    "x = np.random.uniform(low=-1, high=1, size=N)\n",
    "x.sort()\n",
    "x = x.reshape(-1, 1)\n",
    "#计算之前所述的X\n",
    "X = []\n",
    "for i in x:\n",
    "    temp = L(Qf, i)\n",
    "    X.append(temp)\n",
    "X = np.array(X)\n",
    "#差生误差项\n",
    "epsilon = np.sqrt(sigma2) * np.random.normal(size=N)\n",
    "#计算Y\n",
    "Y1 = X.dot(a.T)\n",
    "Y = Y1 + epsilon\n",
    "\n",
    "\n",
    "#### Step 2:拟合数据\n",
    "\n",
    "#对一个数据特征转换,将x转换为(1,x,...,x^k)\n",
    "poly2 = PolynomialFeatures(2)\n",
    "poly10 = PolynomialFeatures(10)\n",
    "\n",
    "#特征转换\n",
    "X2 = poly2.fit_transform(x)\n",
    "X10 = poly10.fit_transform(x)\n",
    "\n",
    "#计算结果\n",
    "w2 = inv(X2.T.dot(X2)).dot(X2.T).dot(Y)\n",
    "w10 = inv(X10.T.dot(X10)).dot(X10.T).dot(Y)\n",
    "\n",
    "\n",
    "#### Step 3:计算结果\n",
    "\n",
    "#构造被积函数,a为系数\n",
    "def E(x, w, a, sigma2):\n",
    "    \"\"\"\n",
    "    被积函数\n",
    "    \"\"\"\n",
    "    #计算f(x)\n",
    "    #n为勒让德多项式次数\n",
    "    n = len(a)-1\n",
    "    l = L(n, x)\n",
    "    f = a.dot(l)\n",
    "    \n",
    "    #计算g(x)\n",
    "    X = np.array([x**i for i in range(len(w))])\n",
    "    g = X.dot(w)\n",
    "    \n",
    "    return (g - f) ** 2 / 2 + sigma2\n",
    "\n",
    "E2 = quad(E, -1, 1, args=(w2, a, sigma2))[0]\n",
    "E10 = quad(E, -1, 1, args=(w10, a, sigma2))[0]\n",
    "\n",
    "print(\"E2=\" + str(E2))\n",
    "print(\"E10=\" + str(E10))\n",
    "print(\"E10-E2=\" + str(E10 - E2))\n",
    "\n",
    "#### Step 4:作图\n",
    "Y2 = X2.dot(w2)\n",
    "Y10 = X10.dot(w10)\n",
    "\n",
    "plt.plot(x, Y1, label='无噪音')\n",
    "plt.scatter(x, Y, label='有噪音',s=3)\n",
    "plt.plot(x, Y2, label='g2')\n",
    "plt.plot(x, Y10, label='g10')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pickle\n",
    "from numpy.linalg import inv\n",
    "from scipy.integrate import quad\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from helper import process\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['font.sans-serif']=['SimHei'] #用来正常显示中文标签\n",
    "plt.rcParams['axes.unicode_minus']=False #用来正常显示负号\n",
    "\n",
    "\n",
    "#############################\n",
    "##stochastic noise\n",
    "\n",
    "E = {}\n",
    "t = 100\n",
    "\n",
    "Qf = [20]\n",
    "N = np.arange(5, 122, 5)\n",
    "sigma2 = np.arange(0, 2.01, 0.05)\n",
    "q = 20\n",
    "'''\n",
    "#进行实验，因为时间太长，这里注释掉\n",
    "for n in N:\n",
    "    for s in sigma2:\n",
    "        e = np.array([])\n",
    "        for i in range(t):\n",
    "            error = process(q, n, s)\n",
    "            e = np.append(e, error)\n",
    "        E[(q, n, s)] = np.mean(e)\n",
    "\n",
    "#保存数据\n",
    "#with open('stochastic noise.pickle', 'wb') as f:\n",
    "#    pickle.dump(E, f)\n",
    "'''\n",
    "\n",
    "#如果不训练读取数据即可\n",
    "#读取数据\n",
    "pickle_in = open('stochastic noise.pickle', 'rb')\n",
    "E = pickle.load(pickle_in)\n",
    "\n",
    "\n",
    "#读取后横坐标N以及纵坐标sigma2以及对应的差值c      \n",
    "c = []\n",
    "n1 = []\n",
    "s1 = []\n",
    "for i in E:\n",
    "    n1.append(i[1])\n",
    "    s1.append(i[2])\n",
    "    c.append(E[i])\n",
    "\n",
    "c = np.array(c)\n",
    "n1 = np.array(n1)\n",
    "s1 = np.array(s1)\n",
    "\n",
    "n1, s1 = np.meshgrid(n1, s1)\n",
    "result = []\n",
    "for i in range(len(n1)):\n",
    "    n = n1[i]\n",
    "    s = s1[i]\n",
    "    temp = []\n",
    "    for j in range(len(n)):\n",
    "        temp.append(E[(q, n[j], s[j])])\n",
    "    result.append(temp)\n",
    "\n",
    "cm = plt.cm.get_cmap('rainbow')\n",
    "plt.pcolormesh(n1, s1, result, cmap=cm, vmin=-0.2, vmax=0.2, shading='gouraud', edgecolors='face')\n",
    "plt.xlabel(\"Number of Data Points, N\")\n",
    "plt.ylabel(\"Noise Level,sigma^2\")\n",
    "plt.title(\"stochastic noise\")\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "#############################\n",
    "##deterministic noise\n",
    "\n",
    "Qf = np.arange(1, 31)\n",
    "N = np.arange(5, 121, 5)\n",
    "sigma2 = 0.1\n",
    "s = sigma2\n",
    "\n",
    "E = {}\n",
    "t = 150\n",
    "'''\n",
    "#进行实验，因为时间太长，这里注释掉\n",
    "for q in Qf:\n",
    "    for n in N:\n",
    "        e = np.array([])\n",
    "        for i in range(t):\n",
    "            error = process(q, n, s)\n",
    "            e = np.append(e, error)\n",
    "        E[(q,n,s)] = np.mean(e)\n",
    "\n",
    "#保存数据\n",
    "#with open('deterministic noise.pickle', 'wb') as f:\n",
    "#    pickle.dump(E, f)\n",
    "'''\n",
    "\n",
    "#如果不训练读取数据即可\n",
    "#读取数据\n",
    "pickle_in = open('deterministic noise.pickle', 'rb')\n",
    "E = pickle.load(pickle_in)\n",
    "\n",
    "c = []\n",
    "q1 = []\n",
    "n1 = []\n",
    "for i in E:\n",
    "    q1.append(i[0])\n",
    "    n1.append(i[1])\n",
    "    c.append(E[i])\n",
    "\n",
    "c = np.array(c)\n",
    "q1 = np.array(q1)\n",
    "n1 = np.array(n1)\n",
    "\n",
    "n1, q1 = np.meshgrid(n1, q1)\n",
    "result = []\n",
    "\n",
    "for i in range(len(q1)):\n",
    "    q = q1[i]\n",
    "    n = n1[i]\n",
    "    temp = []\n",
    "    for j in range(len(q)):\n",
    "        temp.append(E[(q[j], n[j], sigma2)])\n",
    "    result.append(temp)\n",
    "   \n",
    "cm = plt.cm.get_cmap('rainbow')\n",
    "plt.pcolormesh(n1, q1, result, cmap=cm, vmin=-0.2, vmax=0.2, shading='gouraud', edgecolors='face')\n",
    "plt.colorbar()\n",
    "plt.xlabel(\"Number of Data Points, N\")\n",
    "plt.ylabel(\"Target Complexity, Qf\")\n",
    "plt.title(\"deterministic noise\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 4.19 (Page 161)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from helper import L, E\n",
    "\n",
    "\n",
    "def process(Lambda, Qf=5, N=100, sigma2=1, d=2):\n",
    "    \"\"\"\n",
    "    进行一次实验，Lambda为正则项的系数，Qf为勒让德多项式的次数，\n",
    "    N为数据数量，sigma2为方差，d为特征转换的次数\n",
    "    \"\"\"\n",
    "    #### Step 1:数据准备\n",
    "    #系数ai\n",
    "    a = np.random.normal(size=Qf+1)\n",
    "    \n",
    "    #标准化\n",
    "    k = np.arange(1, 2*Qf+2, 2)\n",
    "    s = (2*a**2/k).sum()\n",
    "    a = a / np.sqrt(s)\n",
    "    \n",
    "    #产生点集\n",
    "    x = np.random.uniform(low=-1, high=1, size=N)\n",
    "    x.sort()\n",
    "    x = x.reshape(-1, 1)\n",
    "    #计算之前所述的X\n",
    "    X = []\n",
    "    for i in x:\n",
    "        temp = L(Qf, i)\n",
    "        X.append(temp)\n",
    "    X = np.array(X)\n",
    "    #差生误差项\n",
    "    epsilon = np.sqrt(sigma2) * np.random.normal(size=N)\n",
    "    #计算Y\n",
    "    Y = X.dot(a.T) + epsilon\n",
    "    \n",
    "    #### Step 2:拟合数据\n",
    "    polyd = PolynomialFeatures(d)\n",
    "    \n",
    "    #特征转换\n",
    "    Xd = polyd.fit_transform(x, d)\n",
    "    \n",
    "    #计算Lasso回归,Ridge回归\n",
    "    #Lasso\n",
    "    lasso=linear_model.Lasso(alpha=Lambda)\n",
    "    lasso.fit(Xd, Y)\n",
    "    \n",
    "    #Ridge\n",
    "    ridge=linear_model.Ridge(alpha=Lambda)\n",
    "    ridge.fit(Xd, Y)\n",
    "    \n",
    "    #### Step 3:计算结果\n",
    "    \n",
    "    El=quad(E, -1, 1, args=(lasso.coef_, a, sigma2))[0]\n",
    "    Eq=quad(E, -1, 1, args=(ridge.coef_, a, sigma2))[0]\n",
    "\n",
    "    return El, Eq, lasso.coef_, ridge.coef_\n",
    "\n",
    "#(a)\n",
    "Lambda = np.arange(0.01,2.01,0.05)\n",
    "El = []\n",
    "Eq = []\n",
    "lasso = []\n",
    "ridge = []\n",
    "for l in Lambda:\n",
    "    result = process(l)\n",
    "    El.append(result[0])\n",
    "    Eq.append(result[1])\n",
    "    \n",
    "plt.plot(Lambda, El, label='Lasso')\n",
    "plt.plot(Lambda, Eq, label='Ridge')\n",
    "plt.xlabel('$\\lambda$')\n",
    "plt.title('$E_{out}$')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "#(c)\n",
    "lasso = []\n",
    "ridge = []\n",
    "for l in Lambda:\n",
    "    result = process(l, Qf=20, N=3, d=5)\n",
    "    lasso.append(np.sum(result[2] != 0))\n",
    "    ridge.append(np.sum(result[3] != 0))\n",
    "plt.plot(Lambda, lasso, label='lasso')\n",
    "plt.plot(Lambda, ridge, label='ridge')\n",
    "plt.title('number of non-zero weights')\n",
    "plt.legend()\n",
    "plt.xlabel('$\\lambda$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 4.24 (Page 163)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "d = 3\n",
    "N = range(d+15, d+116, 10)\n",
    "\n",
    "#计算一次实验结果\n",
    "def process(n, d=3, sigma=0.5, k=0.05):\n",
    "    #生成点\n",
    "    X = np.random.normal(size=(n, d))\n",
    "    #偏置项\n",
    "    bias = np.ones(n)\n",
    "    #合并X和bias\n",
    "    X = np.c_[bias, X]\n",
    "    #正则项系数\n",
    "    k = k / n\n",
    "    #权重\n",
    "    w = np.zeros(d+1)\n",
    "    #生成噪声\n",
    "    epsilon = np.random.normal(size=n)\n",
    "    #生成y\n",
    "    y = X.dot(w) + sigma * epsilon\n",
    "    e1 = 0\n",
    "    e2 = 0\n",
    "    E = np.array([])\n",
    "    #交叉验证\n",
    "    for i in range(n):\n",
    "        X1 = np.r_[X[:i, :], X[i+1:, :]]\n",
    "        y1 = np.r_[y[:i], y[i+1:]]\n",
    "        w1 = inv(X1.T.dot(X1) + k * np.eye(d+1)).dot(X1.T.dot(y1))\n",
    "        e = (X[i].dot(w1) - y[i]) ** 2\n",
    "        E = np.append(E, e)\n",
    "        if(i == 1):\n",
    "            e1 = e\n",
    "        elif i == 2:\n",
    "            e2 = e\n",
    "    return e1, e2, np.mean(E)\n",
    "\n",
    "#(a)\n",
    "#记录每个N对应的e1,e2,ecv\n",
    "E = {}\n",
    "for n in N:\n",
    "    E[n] = []\n",
    "\n",
    "for n in N:\n",
    "    E1 = np.array([])\n",
    "    E2 = np.array([])\n",
    "    Ecv = np.array([])\n",
    "    for i in range(3000):\n",
    "        e1, e2, ecv = process(n)\n",
    "        E1 = np.append(E1, e1)\n",
    "        E2 = np.append(E2, e2)\n",
    "        Ecv = np.append(Ecv, ecv)\n",
    "    #计算均值和方差\n",
    "    mean = (E1.mean(), E2.mean(), Ecv.mean())\n",
    "    var = (E1.var(), E2.var(), Ecv.var())\n",
    "    E[n].append(mean)\n",
    "    E[n].append(var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(b)\n",
    "meanE1 = np.array([])\n",
    "meanE2 = np.array([])\n",
    "meanEcv = np.array([])\n",
    "for n in N:\n",
    "    mean = E[n][0]\n",
    "    meanE1 = np.append(meanE1, mean[0])\n",
    "    meanE2 = np.append(meanE2, mean[1])\n",
    "    meanEcv = np.append(meanEcv,mean[2])\n",
    "plt.plot(N, meanE1, label='e1')\n",
    "plt.plot(N, meanE2, label='e2')\n",
    "plt.plot(N, meanEcv, label='ecv')\n",
    "plt.title('mean')\n",
    "plt.xlabel('N')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(e)\n",
    "varE1 = np.array([])\n",
    "varE2 = np.array([])\n",
    "varEcv = np.array([])\n",
    "for n in N:\n",
    "    var = E[n][1]\n",
    "    varE1 = np.append(varE1, var[0])\n",
    "    varE2 = np.append(varE2, var[1])\n",
    "    varEcv = np.append(varEcv, var[2])\n",
    "plt.plot(N, N, label='$N$')\n",
    "plt.plot(N, varE1 / varEcv, label='$N_{eff}$')\n",
    "plt.legend()\n",
    "plt.show()  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
